Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1755 Excerpt: ...and A, the youngest.: v o J Q_U E S T I O N XLI.!.; '.:. J.-..;. The respective ages of three persons, A, B, and C, of whom is the youngest, and C the eldest, being given; it is required to find the probability, that any one of them shall survive the other twa CAS E K; When the survivor is elder, than the two persons to be survived; (thatjs, if C,be to survive A and 5; this survivorsliip will take place, when the three persons die, either in the order A, B, C; or in the crder B, A, C. Let n be the survivor's complement; and let m, and t, b« the_£ompleJnents of the other two persons A, and B. Then (by quest. 3 c.) the probability of their ) nn dying in the order A, B, C is J 'btm 1 And (by quest.36.) the probability of their' dying in thejDrder£ Therefore, their sum, ii.;).: iii;'f Jor will be the probability of Cs surviving A, and B.,;. COR O I:.,-. If the two persons, that are to be survived, are of equal ages; that is, if A--B; then /--m j and the pro bability required will be.--.. f '.' ''":. ' COR O L. II. If the survivor, and the elder of the persons to be survived, are of equal agea; that is, if B--C; then m--n; and the probability required will be--------J 1 ' F s V" C OR O L. COROL. III. If the three persons are of equal ages; then t--m--n; and the result will become.----)--. ", 3»« / 3 C A,5,E II„........,; When the survivor is, elder than one, an,d younger than the other, person to be survived. This survivorship will take place, when the three persons die, in the order A, C, B; or in the order C, A, B. Let, therefore, the complement of the survivor's life be denoted by m; and those of the two persons to be survived, by«, and /. J,,.Then (by quest 37.) the pro-7 n £ bability of their dying in....
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